1. Technical Field
The present invention relates generally to precision measurement, and more specifically to precision measurement of a phase shift in a periodically excited physical system.
2. Background
There is often a need to make precise measurements of a phase shift in a periodically excited physical system. Such measurements are of interest because the phase shift between excitation and response often provides a sensitive way to measure some property of the physical system, such as its resonant frequency or damping constant, which in turn varies with a quantity to be monitored in the environment, such as temperature or chemical composition.
For example, the physical system can be an optical resonant cavity formed by two opposed, high reflectivity mirrors. The excitation may be the intensity of a modulated incoherent light source that illuminates one of the mirrors; the response may be the intensity of modulated light that leaks out of the cavity. In such case the phase shift between the modulation of the excitation and the modulation of the response varies with photon lifetime within the resonant cavity. That is, it varies with a damping constant, which in turn varies with optical losses caused by the presence of an optically absorptive chemical species in the gas filling the cavity. Such technique may be used to sense the presence of a variety of compounds. For example, if the light has a wavelength in the 440 nm spectral region, optical absorption by nitrogen dioxide may be sensed in this way.
In a further example, the physical system may be a piezoelectric quartz crystal resonator. The excitation may be applied voltage; the response may be resulting current. In such case the phase shift between current and voltage varies with changes in resonance frequency, which in turn varies in response to a factor, such as temperature or mass deposition onto the surface.
In many practical situations, the combination of high excitation frequency and low response intensity make it unfeasible to directly measure the phase shift between response and excitation. In these cases, heterodyne detection has typically been employed to allow the measurement to be made at a lower frequency.
However, some amplification of the response usually is required before the actual phase shift measurement can be performed. This amplification creates problems, in that it generally causes an additional phase shift that must be distinguished from the phase shift caused by the physical system under study.
Accordingly, there is a need for an improved technique for precision measurement of a phase shift in a periodically excited physical system, which is not affected by these shortcomings.